Diffusion tensor imaging (DTI) has shown promise as a noninvasive tool to investigate brain structures. As an application of DTI, "fiber tracking" techniques have been demonstrated to have the potential to delineate neuronal pathways in the brain and connectivity (and its disruption) in neurological disorders. However, there are challenges in existing DTI and fiber-tracking techniques, such as the problem caused by fiber crossing, in which multiple fiber compartments coexist in an image voxel. In this case, the estimation of the tensor components can be seriously biased, preventing fiber-tracking algorithms from following the actual fiber connectivity in the vicinity. A diffusion model beyond conventional DTI and capable of providing more intravoxel information is essential to overcome this problem. We have developed a new method to map intravoxel structures of white matter, especially fiber crossings, using circular spectrum decomposition based on high-angular resolution measurements of apparent diffusion coefficients (ADC). The basic premise of our method is to determine the ADC values voxelwise on the unit circle spanned by the major and median eigenvectors of the diffusion tensor, and then apply a 1D Fourier-transform onto this circle. The 0th, 2nd, and 4th order harmonic components of the circular spectrum provide effective indices for mean diffusivity, linear fiber, and orthogonal fiber crossing diffusion respectively. A theoretical frame work has been established for the novel diffusion imaging technique. Simulations on a digital phantom demonstrated the effectiveness of the technique to identify fiber intersections. In vivo experiments on normal subjects showed that high 4th-order components (fiber crossings) can be observed in a number of brain regions, including pons, medulla, and areas around corpus callosum. This new technique provides an innovative tool for mapping fiber crossings inside the brain. Information obtained from this technique would be used for improving fiber-tracking techniques and for better delineating neuronal pathways under normal and pathological conditions.